Download Two ways of looking at a transformer

The Rules of Electromagnetism
What is Magnetism ?
It is easier to explain what it does !
1. It causes magnets to align themselves in a particular direction (“Northseeking poles” etc)
2. It causes current-bearing conductors to experience forces if conductor and
field are not parallel. (F = Bil if conductor and field are at right angles to each
other).
3. It induces e.m.f.s in conductors moved through magnetic fields (unless any
two of conductor, field and motion are parallel). (e = Blu if all three are at
right-angles).
4. If the field is changing with time, it induces an e.m.f. in any loop of a circuit
through which it goes. (e = n d/dt).
5. It is suspected (though the evidence is inconclusive so far) that alternating
magnetic fields, especially very high-frequency ones (e.g. mobile phone
transmissions !) may have adverse effects on health (see below).
“Magnetic fields” are produced by currents (Corkscrew Rule). It there is just
one wire, the field is such as to cause a magnetic pole to orbit the wire and its
strength H (magnetising force) is I/(2r) where I is the current and r is the
distance out from the wire. The Magnetic Flux Density B is given by 0rH
where is the permeability of free space (4 x 10-7 H/m) and is the number of
times more permeable to magnetic flux the particular material is compared to
free space (the Relative Permeability). H is called the magnetising force and it
is equal to the MMF (see below) divided by the length of the path traversed by
the magnetic flux. If we make a coil of the wire, we concentrate the magnetic
flux through the coil and its strength now depends on the number of turns in
the coil times the current. The magnetic flux is considerably increased by
causing it to flow through a ferromagnetic material (e.g.iron) rather than
through air, plastic etc. In this respect, 1 mm of air presents about the same
obstacle to the flux as several metres of iron, so electric motors are carefully
constructed to minimise the "air gaps" through which the flux has to pass.
To gain an idea of how many turns etc. we need, we will do a few simple (?)
sums.
The magnetic flux density 0.1 m from a wire carrying 1 A in air will be 0 x
1/(2 x 0.1) = (4 x 10-7) x 1/(2 x 0.1) = 2 x 10-6 T. This flux density can
cause a force of BIL = 2 x 10-6 x 1 x 0.1 = 2 x 10-7 N to act in an 0.1-m long
wire carrying 1 A. This does not seem to be a very large force, so we need
either lots of wire, or more current, or a stronger field, or preferably all three, if
we are to make a useful electric motor ! It turns out that by using iron and
hundreds of turns of wire we can produce flux densities up to perhaps 1 T.
Our 0.1-m long wire would then have experienced a force of 0.1 N, which is
still not massive but we could again increase it by using many wires in a coil
rather than just one. (More om motors etc. later).
Radio waves involve both electric and magnetic fields interacting (the exact
mechanism is quite involved !) but, apart from microwave ovens (which
normally cook only the food), the combination of frequency and power has not
until recently been high enough to cause significant adverse biological effects.
Mobile phones are under some suspicion especially because
i) the received power is proportional to the transmitter power divided by the
square of the distance from the transmitter, and
ii) the phone is so near to the brain whilst it is transmitting.
The mechanism is likely to be the heating effect within the brain.
I have tried to find some typical figures for mast and user transmitter power,
but I have so far been unsuccessful. The following evidence has come to
light:
i) During a user test, users who continuously used a mobile phone for an hour
or more became disoriented and confused (though this may not have any
relevance whatever to the transmitted radio waves !)
ii) There is some evidence from animal experiments that brain cells are
susceptible to mutation by fairly strong high-frequency radio fields.
iii) A friend who works for an electricity company in Berkshire measured the
r.f. field strength from neighbouring masts and at about 250 mm from a
mobile phone. The mast transmissions hardly registered on his instrument at
all but the phone one produced an almost full-scale reading.
iv) Most of the radiation is transmitted sideways from an aerial, so, if your
offspring's school is to have a base-station mast erected on the premises, the
roof is BY FAR the best place to put it ! Measurements near such a school
showed that the transmissions from other masts were stronger in the vicinity
of the school than those from the mast on the roof. If you feel like
demonstrating, you should perhaps demonstrate for it to be put on the roof
rather than at the edge of the sports field !
v) Much of the r.f. radiation falling on a building is absorbed by the walls and
roof, especially at the higher radio frequencies.
vi) The Director of the National Radiological Protection Board appeared on
television some years ago in connection with a school-grounds-located mobile
phone mast. He stated that its transmissions were not definitely known to be
safe but pointed out that the Radio 4 signal in the vicinity (also not of proven
human safety as he pointed out) was of comparable strength to that from the
mast.
vii) As we move further from the source of the radio transmission, the strength
of the "field" diminishes approximately according to the Inverse Square Law.
This means that the strength of the signal at a distance x from the
transmitting antenna is given by FRED/x2 where FRED is a constant
depending on the transmitter power.
(You may like to visit the website http://www.doh.gov.uk/mobilephones for
more on the above).
Example .. what will the field strength be (a) 3 metres from a mast for which
FRED = 10 units, (b) at a distance of 200 metres from such a mast, (c) in the
centre of the head of a user of a mobile phone for which FRED = 1 unit ?
Some main electric motor types
1. The d.c. motor
Basically simple .. the magnetic field is supplied either by a permanent
magnet (small motors) or by a current-carrying coil as above. The rotating
assembly (known as the Armature) is supplied with current via the
Commutator and the Brushes which make a sliding contact with the
commutator. The purpose of the commutator is to reverse the armature
current every half-revolution to ensure that the torque exerted on the
armature continues to act in the forward direction. The sparking from the
reversal of the current as well as the sliding contact causes wear of the
brushes and commutator, which is a significant drawback of d.c. motors.
The field can be supplied by a permanent magnet (usual in small batteryvoltage motors), a coil in parallel with the supply ("shunt motor") or a coil in
series with the supply ("series motor"). The latter is still often chosen for
traction applications where its high starting torque is very useful.
Electric generators are actually the same machine as electric motors; in a
generator, the generated voltage is higher than the terminal voltage, whilst it
is lower in a motor where it is called the Back e.m.f. The back e.m.f. is
calculable from "e=Blu" and it is therefore proportional to the motor speed if
the field and dimensions are constant.
a.c. motors
The usual a.c. motor is the three-phase induction motor which, in its usual
"squirrel-cage" form, requires no electrical contact between the rotating part
(the rotor) and the stationary part with the field windings (the stator); the rotor
current is induced by transformer action. The cage motor has a torque-speed
graph which peaks at a speed near to the rotational speed of the induced
magnetic field in the stator, so it has an inherently poor starting torque
(though we can improve it by using a variable-frequency supply from a powerelectronic converter).
Such induction machines are also used as generators in conjunction with
wind-turbines, but the "mainstream" generator is the synchronous type in
which the rotor coils carry a direct current. The "NP/Powergen" version always
generates at 50 Hz (so constant-speed) but similar machines are also the
standard generator in vehicles and, amazingly enough, railway IC125 power
cars ! In both the latter two examples the frequency does not matter as the
a.c. output is rectified anyway.
The usual power-station generator is the three-phase alternator in which a
d.c. electromagnet is rotated such that its magnetic flux passes through three
sets of coils in turn .. inducing the three a.c. voltages.
The transformer
This very useful device consists of a magnetic core (usually laminated iron or
ferrite) with two coils of wire wound on it such that the magnetic flux produced
by one coil (the Primary Coil) also goes through the other coil (the Secondary
Coil).
V1
I1
I2
V2
If there is no flux leakage V1 = n1d/dt and V2 = n2d/dt, so n1/n2 = V1/V2.
If it is an ideal transformer, no power is produced or dissipated in it, so
(forgetting phase for simplicity) V1I1 (the input power) = V2I2 (the output
power) .. so our equation for the voltages and currents can be extended to
n1/n2 = V1/V2 = I2/I1.
Some examples
1. What will be the magnetic flux density at ground level immediately beneath
a power line 15 metres above the ground carrying 1500 A ? How does this
strength of field compare with the earth's field ?
2. A particular electrical machine has a magnetic flux density of 0.8 T through
its main rotor/armature conductors each of which is 0.3 m long. The rotor
diameter is 0.2 m. The conductors may be assumed to be level with the
outside of the rotor. If each conductor carries 5 A, how many conductors will
be needed to give a torque of 10 N m ? What back e.m.f. will be generated at
a speed of 2000 rev/min ?
3. A 240-110 V transformer has 2400 primary-coil turns.
How many secondary turns will it have ?
If the mains voltage were only 230 V, what would the transformer output
voltage be ?
Bill Barraclough
October 2001 (amended April 2002)